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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

The Laguerre pseudospectral method for the two-dimensional Schrödinger equation with symmetric nonseparable potentials

Haydar Alıcı
Pages
539–552
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrödinger equation on the whole real plane.
📊
Key Findings & Data:The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrödinger equation on the whole real plane.
💡
Conclusion & Impact:However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:The Laguerre pseudospectral method · two dimensional Schrödinger equation · symmetric potentials

Abstract

The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrödinger equation on the whole real plane. However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.

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Cite This Article

Alıcı, H. (2022). The Laguerre pseudospectral method for the two-dimensional Schrödinger equation with symmetric nonseparable potentials. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 539–552. https://ajindex.com/articles/529680

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